<h3>How to Solve The Constant of Proportionality of a Non Proportional Graph?</h3>
We apply our knowledge on the direct and inverse variations, identify them and then determine the constant of proportionality and thereby get the solutions to our problems.
Example 1:
Find the constant of proportionality, if y=24 and x=3 and y ∝ x.
Solution: We know that y varies proportionally with x. We can write the equation of the proportional relationship as y = kx. Substitute the given x and y values, and solve for k.
24 = k (3)
k = 24 ÷ 3 = 8
Therefore, the constant of proportionality is 8.
Example 2:
4 workers take 3 hours to finish the desired work. If 2 more workers are hired, in how much time will they complete the work?
Solution:
Let x1 = number of workers in case 1 = 4
x2 = Number of workers in case 2 = 6
y1 = number of hours in case 1 = 3
y2 = number of hours in case 2 = To be found
If the number of workers is increased, the time taken to complete will reduce. We find that number of workers is inversely proportional to the time taken, (y1 = k/x1) ⇒ 3 = k / 4⇒ k = 12
Again, to find the number of hours, (y2 = k/x2) ⇒ y2 = 12/6 = 2 hours.
